Can one tell a lie to non-religious Jews to get them to keep Shabbos? Everything that I
regard as central to Judaism tells me that the answer is "no". Not only do I, a
halachic layperson, think this, but also rabbonim that Ive consulted say
unequivocally that something you even suspect may be false should not be used as part of
The Torah codes debate forces us to face this issue squarely. There are those who
assert that it has been statistically proven that there are codes in the Torah so it can
be used as a first step to get some non-religious Jews to start thinking seriously about
yiddishkeit. But the virtually unanimous opinion of those professional mathematicians and
statisticians  who have carefully examined the
evidence is that there has been no scientific proof of the codes.
Those who remember my earlier article will note a change in the six months  between my writing that piece  and this one, I have spent considerable time studying the evidence  and the replies of the proponents (both in Jewish
Action and on the web) and I have gone from being skeptical about the arguments presented
for the validity of the codes to being certain that all of the evidence presented so far
has no legitimacy . My first goal here will be to
explain why I and many other scientists have reached this conclusion. Then Ill
address some of the other points raised in the articles of Rabbi Mechanic and Mr. Witztum . Finally, Ill turn to the key issue of what the
scientific community has to say of what is, after all, claimed to be a scientific proof.
Recall that the codes are based on searching for equidistant letter sequences (ELSs),
that is words occurring in the text of the Torah but with skips between the letters, for
example in the 6th, 12th, 18th,
letter after an initial letter (the skip in this
case would be said to be 6). Some, but not all of the time, the codes searchers look for minimal
ELSs with the skip as small as possible .
The codes Ill discuss here are of two distinct types: clusters of words  near each other, and the famous Rabbis
experiment  which appeared in the journal Statistical
Science . There are three  fundamental problems with the codes:
- Any text of similar size will have similar clusters of words to those found in the
- The probabilities quoted for the word clusters are computed by methods contrary to
the accepted laws of probability and used in situations where it is essentially impossible
to assign meaningful probabilities.
- The famous Rabbis experiment has many flaws in both its data and in its method. The
largest flaw, one that, by itself, already entirely explains what was found, is the
subjective nature of the list of appellations used for the Rabbis.
I intend to address each of these points in turn and then the issues of whether there
is a mesora for minimal ELSs, the significance of publication in Statistical Science, and
finally, the view of the scientific community towards the issue of validity of the codes
Problems with Word Clusters
The first two fundamental problems with the codes deal with word clusters. Let me
explain what I mean by point 1, which says that any text of similar size will have
similar clusters of words to those found in the Torah. Then Ill present four
illustrative examples. It is critical to note that the word used before
"clusters" is "similar" and not "same". After finding
something in the Torah, codes proponents are fond of pointing out that they looked for the
same thing elsewhere and didnt find it. Thats not surprising at all
because it is only similar clusters that will be found elsewhere, not the exact
same words. These phenomena invariably depend on what scientists call degrees of freedom
and which Ill refer to as wiggle room.
The point is that the searcher can make many choices in looking for codes. For example,
if you are looking for holiday clusters, which holiday do you look for and once you pick
the holiday, say Chanukah, which words do you look for? In a Chanukah cluster, you could
look for names of the Maccabees and other historic figures, words connected with the
Temple, words connected with miracles in general, words connected with candles or even
words like latke, dreidl and sufganyiot. Moreover, the Hebrew language multiplies each
possibility into many. Do I place a hey (for the definite article) in front? Do I include
the extra yuds and vavs that can occur in variants of some words?
It is the wiggle room that allows an ELS cluster to be found in the Torah and its
the same wiggle room that allows an ELS cluster to be found in other texts. But the very
nature of wiggle room is that you have freedom in choices so the precise alternatives
necessary to get the cluster in one text will be different from the alternatives
needed to find something in another text. The clusters in the two texts will be similar
but not the same. The quality of the clusters will be largely determined by the
creativity of the searcher rather than by anything intrinsic to the underlying text.
As a first example of this phenomena, please consider the following figure, which is an
impressive cluster of words associated with Chanukah.
The phrase that anchors the cluster is the ELS for Ner Chanukah (Chanukah candle) which
starts from the lower right (last line) and swings up on a diagonal every fourth line . It is a minimal ELS in the entire text from which
this picture is a fragment. The other words are all minimal (in the entire text) ELSs of
Chanukah related words, for example, Menorah. Chanukah clusters have been a popular topic
with codes searchers and none has more words within a short space than this one .
This example is an impressive cluster that might lead you to suspect that it
didnt occur by chance. However, you should know that it is not a code in the Torah
but rather a code in the Hebrew translation of War and Peace .
As a second example, consider one of the most charming of the codes. The names of 25
trees were found  in the section of
Bereishit  where the Garden of Eden is described.
They were all found as ELSs (although not minimal ELSs) in this section. Dr. Brendan McKay
 took that same section and did 100 random
permutations  of its letters and found that all
25 tree names still appeared as ELSs in 58 out of the 100. I did the same test on War
and Peace using the section of the document that started at the exact same letter
position and had the same length . I found that
all 25 tree names appear in this analogous section of War and Peace. I also found
out of 100 random permutations that 59 had all the names (and each one of the hundred had
at least 23 names.).
Ive met many people who expressed amazement at the very existence of all these
words in the one section of Bereishit. Our initial tests show that this fact alone has
absolutely no significance. We then looked more closely at Prof. Michelsons article
and saw that he said that since the words are short, one shouldnt be as surprised at
the occurrence of all these words as by the fact that they are in ELSs with especially
short skips. Indeed, he estimated the probability of the trees appearing as such short
ELSs was 1 in 100,000.
So Dr. McKay and I decided to do some additional research on the subject. First we
decided to measure the size of a set of ELSs by the total sum of the skips of the
individual words. We did the test with the original Bereishit text and original War and
Peace text and 1000 permutations of each. The actual Bereishit text scored in 8th
place out of the 2002 sample texts. That implies that an estimate  for the probability is about 1 in 125, a far cry from the 1 in
100,000 but still something that appears to have some significance.
But before we could be sure of this significance, we needed to examine whether perhaps,
the phenomenon could be explained by degrees of freedom that are present. There are two
obvious places where one might think there are possible choices exactly which trees
to search for and how to spell them. Prof. Michelson explained that Prof. Rips took all
of the trees found in the Torah according to the book The Fauna and Flora of the Torah
by Yehuda Feliks. In addition to looking in the book, we decided to consult Prof. Feliks,
who is, after all, a recognized expert on this subject.
A friend of mine met with Prof. Feliks in Jerusalem who informed us that first of all,
there were three trees from the Torah missing from the list, and, secondly, that some of
the spellings used differed from those in his book. For the three additional trees
(Comiphora Africana, Astragalus, Cinnamon), we found that one doesnt even occur as
an ELS in that section of Bereishit and that the other two occur only as very long ELSs.
Dr. McKay then redid the experiment  with the
spellings provided by Prof. Feliks (only using those trees that occur as ELSs) and out of
2002 permutations, the actual Bereishit text ranked 235. This 1 in 10 ranking is at a
level that statisticians never regard as statistically significant. We concluded that
wiggle room can explain the apparently significant result obtained by Prof. Rips and
quoted by Prof. Michelson.
As a third example, I mention a challenge of Michael Drosnin  who stated in a Newsweek interview on June 9, 1997:
"When my critics find a message about the assassination of a prime minister encrypted
in Moby Dick, I'll believe them." So Brendan McKay looked there and found  clusters based on the names of Indira Ghandi, Rene
Moawad, Leon Trotsky, Martin Luther King, Chancellor Engelbert Dollfuss, Sirhan Sirhan,
Abraham Lincoln and Yitchak Rabin. For example, McKay found Abe, Lincoln and
bang as ELSs near the plain text word killed. 
Sometimes people ask me about Rav Weissmandls examples. Here is Aish
haTorahs position on his ELSs  : "Only
one or two of Rabbi Weissmandls word patterns are presented at Discovery, for the
pedagogical purpose and process of showing that they are NOT Codes (i.e., word patterns
that were deliberately placed in the Torah by G-d) and how one can be easily fooled into
thinking that they are, and how referring to these accidental patterns as
Codes is sheer nonsense". It is unfortunate that by using Rav
Weissmandls codes for something for which they were not intended, Aish has decided
that it is necessary to kill them.
Mr. Witztums Closing Example
In my original article, I said: "Doubts that I may have had about publishing my
conclusions are overridden, I feel, by a gemara in Shabbos, which says, The seal of
HaKadosh Baruch Hu is Truth.". Mr. Witztum, in his reply, presents what he
says is this concept encoded as in ELS in Bereishit. He found the Hebrew word for seal and
variants as plain text near an ELS for Elokim Emes and quotes a very small probability for
what he found  . As my fourth example of wiggle
room in word clusters, Ill consider this example .
The quote I used appears three times in the Babylonian Talmud with those exact words. I
have no idea what Mr. Witztum did or didnt look for, but it is clear if he was
seeking that quote what he should have looked for are ELSs for seal, truth and HaKadosh
Baruch Hu near each other. In fact "HaKadosh Baruch Hu" is 12 letters, too long
to expect to be found as in ELS in Bereishit. Indeed, it is not found. Thats OK
because the abbreviation HKBH is standard . But
searches for this abbreviation against variants of seal and truth yield no ELSs especially
near each other.
Were Mr. Witztum a codes researcher as he claims, hed have informed us that he
tried that search and it failed. But hes a code searcher rather than an impartial
researcher. His method seems to be to keep searching until he finds something. With this
attitude, the probability that hell find something to report on is one out of one,
not one out of millions.
So instead of searching for my original quote, he searches for something which is
conceptually related but with rather different words. You should note in passing that
Elokim Emes is usually translated as saying that G-d, Himself, (not his seal) is True. You
should also note that while words in most of Mr. Witztums clusters are ELSs, in this
case he takes some of the words as plain text because the example doesnt work if one
looks for ELSs for each of the phrases. But most of all, you should note that once one
allows oneself to use an alternate name to HKBH, there are many other possibilities
for example, he could have looked for Elokim Chayim, Melech Olam, or HaShem Elokim. You
should now understand what wiggle room is.
No doubt, faced with this criticism, Mr. Witztum could (and perhaps will) produce a
story explaining why it was reasonable to search for this particular combination although
he didnt do that in his Jewish Action article. Just as one could find a story for
Elokim Chayim, Melech Olam, or HaShem Elokim. You can always find a story once you locate
Problems with Calculations of Probabilities
Word clusters as presented by Mr. Witztum and other codes proponents are often
accompanied by reports of fantastic probabilities. The second basic fact is that these
probabilities are computed by methods contrary to the accepted laws of probability and
used in situations where it is essentially impossible to assign meaningful probabilities.
The other basic points require little mathematical sophistication to understand, but
because the correct calculation of probabilities is a subtle science, I cannot explain
this fully here since I dont think you want to read a textbook on Probability
Theory. So Ill have to settle for trying to briefly explain the most serious error
and give pointers to the mathematically knowledgeable reader of what some of the other
issues are. This is one place where Im going to have to ask you to rely on the
judgement of those professionals whose job it is evaluate mathematical arguments.
A key issue involves the notion of independence. Flip a coin ten times and write down
the results as a string of Hs and Ts. The probability you get the string HHHHHHHHHH is 1
in 1024, that is one half times one half times one half times
(ten times). Now flip
a coin one time and write down the result of that single flip ten times, repeating the
same letter. The probability of HHHHHHHHHH is exactly one half. The difference, of course,
is that in the first case, the letters are independent of one another while in the other
they are highly dependent. In real life, things are rarely totally independent nor totally
dependent which make the calculations of probabilities exceedingly difficult.
Invariably, the large numbers in Mr. Witztums calculation rely on multiplying
together lots of not so large numbers (as in the above case one gets 1024 by multiplying 2
times itself ten times) by assuming independence but in situations where independence is
not a valid assumption.
Besides assuming independence in situations where it is not valid, the codes
proponents calculations suffer from other problems ,
- they either ignore the "wiggle room" or consider a very, very small subset of
- they are a posteriori rather than a priori  (I discussed this in my Jewish Action article)
- they sometimes use as a base the minimal text that contains the cluster rather than the
text actually searched.
But you neednt take my word on the fact that clusters have no statistical
significance. Consider these two quotes:
- "The only statistically significant ELSs (i.e., Codes) that have been discovered so
far are the statistically verified Rabbis example"
- "Other examples are presented (Sadat, Diabetes, Gulf War, etc.) that employ the
same methodology as Witztum's Famous Rabbis experiment but, for technical reasons, cannot
be statistically measured. This limitation is made clear and they are presented only as a
lead-up to, and an explanation of, the methodology used for the Famous Rabbis
These quotes are from Aishs Discovery Seminar website .
The Nature of the Famous Rabbi's Experiment
Before turning to the most serious flaw in the Famous Rabbis experiment, I want to make
sure the reader understands the nature of the evidence since it is really very different
from the simple word clusters discussed so far .
In the article referenced in footnote 10 that Ill call WRR, the authors looked at
appellations and dates associated to 32 moderately famous Rabbis. By appellations, I mean
some of the manifold ways that Rabbis are called. Consider, for example, the Rambam and
the Chofetz Chaim, appellations for Moshe ben Maimon and Yisroel Meir Kagan and
youll understand what is meant by an appellation. Most personalities have multiple
appellations, for example, in WRRs parallel very famous Rabbis list, the Rambam
appears as HaRambam and Rabbi Moshe .
They took appellations of the Rabbis and their dates of birth and/or death and looked
at the correlations between their ELSs and found a high statistical correlation for these
lists in Bereishit but not in the test text of War and Peace.
You need to understand that the evidence is purely statistical. Many people Ive
talked to left codes presentations with the impression that all 32 Rabbis
names were found close to their dates of birth or death. This is not so . For example, taking into account multiple dates and appellations,
there are 298 pairs. Of these 135 (45%) dont even occur as ELS pairs.
WRR assign a number between 1/125 and 1 to each pair that they call the c-value with a
small c-value indicating closeness and a large value less closeness. In essence, their
evidence is that considerably more than a fifth of the remaining pairs have a c-value
between 0 and 0.2, indicating closeness. But 8 of the pairs have a c-value between 0.8 and
1.0 so that it is certainly not true (even after throwing out the 45% of examples that
dont occur at all) that all the Rabbis appellations appear near their dates.
Moreover, Dr. McKay did an interesting test. He took the minimal ELS for HaRambam
(the version of the name that WRR use) and looked for its distance (using WRR c-values)
from all the dates of the year using the WRR form of dates. Of the 1064 possible
dates , only 930 occurred as ELSs and he ranked
these dates in c-value order against Rambams name. When he looked at distances for
the four dates of Rambams birth and death that are among the 930, he found they
ranked at positions 332, 686, 696 and 890. So Rambams name does not occur at all
close to his dates of birth and death compared to other dates.
You should also know that the c-values are defined in a rather indirect way that
doesnt strictly correspond to our intuition of closeness. It is theoretically  possible for a pair of words with the minimal ELS
for one totally in the parsha of Bereishit and the other in the parsha of Vayechi  to have a c-value of 1/125 (as close as possible
according to c-values) and it is also theoretically possible to have two minimal ELSs
which intersect and have a c-value of 1 (as far apart as possible according to c-values).
The definition of c-value is extremely complex. If I were attempting to assign a
distance between the encodings of two words, Id look for them as minimal ELSs and
measure the number of letters between the centers of those ELSs. This simple-minded method
involves computing a single distance in the text. In contrast, the WRR method of computing
c-value, of say two 5 letter words typically involves not 1, not 2, not 10 or 20 but the
computation of over 6 million distances. You read that right over 6 million .
Id emphasize that neither the purely statistical nature of the evidence nor the
complex method of measuring closeness are central to the issue of the scientific validity
of the experiment. But they raise two kinds of questions. The first is theological: if
HaShem placed this evidence there, would he do it such an incredibly indirect and
imperfect way? After all, the Torah represents Truth, not truth in some average
The second is that the complexity of the experiment suggests that the result may be
sensitive to changes of the method of measuring distances and the statistical method used . Indeed, Prof. Haralick (whom Rabbi Mechanic
identifies as having positive leanings towards the codes) has redone the WRR experiment
using a different method of measuring distances that he arrived at with his vast
experience in pattern recognition. He also changed the method of statistical analysis but
he used the same lists of dates and appellations. The probability dropped from the 1 in
62,500 quoted by WRR to only 1 in 400 . This
level is one that is at best marginal for tests of statistical significance. More
importantly, it was arrived at by only varying the method. Im about to claim that
the data WRR use is seriously flawed. Prof. Haralick found a substantial decrease in
probabilities by varying the method without even changing the most faulty part of the
The Fatal Flaw in the Famous Rabbis Experiment
Now I turn to the data in the famous Rabbis experiment and the most serious problem
with the WRR paper. While there are legitimate questions about the choice of dates, the
place of the most significant wiggle room, which as well see can totally explain
what was found, is the list of appellations that WRR used.
On its web site, Aish has put
its finger on what is needed for a test to be scientifically valid : "
The words to be searched for must be derivable by a priori
specified and repeatable methods". The list must be objective so that another
researcher can replicate the choices in the list. It should not be based on subjective
Lets see what WRR have to say about the choice of the list of appellations. Their
main statement is that "The list of appellations for each personality was provided by
Professor S. Z. Havlin, of the Department of Bibliography and Librarianship at Bar Ilan
University, on the basis of a computer search of the Responsa database at that
university". They also provide four spelling rules that they use but that is all they
say about how the list was constructed.
When mathematicians began to seriously look at the details, many questions were raised
for example, it turns out that for 12 of the 32 Rabbis, Prof. Havlin didnt
use the Responsa database . In response to a list
of queries, Prof. Havlin provided a statement
with various details about his construction of the list .
Prof. Havlins testimony makes it clear that the list is not objective. That is, two
well-meaning scholars starting from scratch and working independently would arrive at very
different lists. He calls a large section of his document "Professional
Judgements" and says he had to use discretion in making choices. Not even in Alice
in Wonderland would a list that required judgements on the part of the list maker be
called objective. Indeed, since he says in several places that he cant recall why he
didnt include certain names, it is clear that not only wouldnt the list be the
same if another scholar produced it, it wouldnt be the same if the same scholar
produced it ten years later.
Along the way, Prof. Havlin poses a large number of rules, many of which are clearly
arbitrary. For example, he states that appellations must be pronounceable to be included?
Why? Any Talmudic student seeing the letters beis-yud, would know that the Bais Yosef
(Rabbi Yosef Caro) is intended. But Prof. Havlin says that this isnt a legitimate
appellation because it isnt pronounceable. If HaShem placed Rabbis names in
the written Torah, why would He fail to use the most common written
nicknames for those Rabbis? The pronouncability rule is an arbitrary one that another
scholar making the list might not use. In addition since the rules have only been made
explicit years after the experiment was published, the lists also lack the property of
being a priori.
It is critical to realize that the choice of rules in making the list is as much a part
of making the list as then applying those rules. Once the list is subjective, the
experiment becomes a test of the list, not of Bereishit. Rabbi Mechanics clear
criteria, with which the scientific world would agree, that the method must be repeatable
is violated. The experiment isnt valid science.
You might wonder though if the wiggle room provided by the subjective nature of the
list of appellations is enough to explain the striking results of WRR. And here the
interesting paper of Bar-Natan and
McKay  (henceforth BNMK) provides the answer.
They produced another list of reasonable appellations, many of them in common with the WRR
Recall that WRR found that the WRR list had a statistical correlation with the dates
when looked for in Bereishit but not in War and Peace. Similarly, BNMK found that
the BNMK list had a statistical correlation with the dates when looked for in War and
Peace but not when looked for in Bereishit. The correlation that BNMK found in War
and Peace for their list was as statistically significant as what WRR found in
Bereishit for their experiment. So BNMK show that the wiggle room in the list is indeed
enough to totally explain the phenomenon observed by WRR.
Mr. Witztum has a long reply posted
on the web trying to explain why the WRR list is valid and the BNMK list is not .
It is totally unconvincing because it again
depends almost entirely on reference to arbitrary rules. One clear example of the issues
concerns whether the name of Rav David Oppenheim when written in Hebrew characters has one
yud or two yuds before the final mem. WWR use one yud while BNMK use two. The original WRR
paper told us that the list was prepared by searching the Responsa database. So
what does this database say about this variant spelling? The one yud version used by WRR
appears twice in the Responsa database. The two yud version that BNMK use appears over 30
times including as a signature in some of the responsa written by Rav Oppenheim. How does
Mr. Witztum defend this? He cant use the four rules that appear in the original WWR
paper nor the dozen plus rules that are implicit in Prof. Havlins letter since none
of them applies to this case. So he invents a new rule about how one should transliterate
words whose original was German. I ask you: If Rav Oppenheims name were encoded in a
special way in Bereishit, do you think it would use the spelling Rav Oppenheim used in his
own responsa or would it use a variant that Mr. Witztum decided was correct on the basis
of some arbitrary rule he made up? 
On the Issue of Honesty
Mr. Witztum has said that Im secretly accusing him of dishonesty and Rabbi
Mechanic claims that I am calling their list "manipulated". That is not true. I
have no need to consider the issue of honesty because it is irrelevant. Once the list is
seen to be subjective, the case of whether this is scientific proof is closed (it is not)
and the issue of whether the list was arrived at in an honest way or dishonest way, with
or without unknown bias, becomes moot. Indeed, if I had firm evidence that they had
cheated, I could not publicly present it on account of the laws of lashon hora. The
experiment is seen to be invalid on the basis of Havlins own testimony that the list
is subjective, so what purpose would there be in my exposing the evidence of dishonesty? 
It is important to realize that it is precisely because of this issue of "Are you
accusing me of dishonesty or of unintentional bias?" that science demands
repeatability in experiments. There are too many examples in the history of science of
researchers fooling themselves and/or others when they do a subjective analysis. For this
reason, science has to reject situations where the result depends entirely on presumed
honesty of the research because independent researchers cannot repeat the entire
experiment independently. Once researchers have to say "Dont you believe
were honest?" theyve admitted that the research involves subjective
elements and so admitted that their experiment is flawed.
There is a further element to consider. Is it really sound to approach someone who is
struggling with the issue of faith that the Torah is divine with the notion that you have
a proof of this cardinal point of faith if only they will have a different kind of faith
-- that some researchers were honest?
A comment on the Nations Experiment
When I met with Professor Rips in Jerusalem, he agreed that there were lots of degrees
of freedom in the famous Rabbis experiment, which could raise questions. He urged me to
instead look at paper
he gave me, also by Witztum, Rips and Rosenberg ,
which contained what he called the Nations experiment .
This paper looked for correlations in the sense of the original WRR paper between the
names of the 70 nations from Parshat Noach and ELS for the phrase <attribute+nation>
for certain attributes . Their test claimed that
the possibility of what they found occurring by chance is 1 out of an astounding 250
There are a myriad of possible attributes you could look for for instance
language of Magog, King of Magog, leader of Magog, and religion of Magog but Rips said
they picked the attributes mentioned in the writing of the Vilna Gaon so there were no
degrees of freedom in the problem. Of course, this ignores the biggest source of wiggle
room why look at the writing of the Gaon and not some other authority (and why look
at the particular writing of the Gaon that they picked the Gaon wrote about
attributes of the Nations at least four times). But lets see if there is any other
wiggle room. Here is an exact quote of what this paper says:
"Jewish tradition further tells us (Hagra, 1905), that a nation has the following
- its name,
- its country,
- its language,
- its script."
They proceed to use the word sfat for language. But the writing of the
Gaon  uses lshon, not sfat.
Theres part  of the wiggle room. Does it
make a difference? To eliminate the impact of the other problems in the paper, I asked
McKay to do a test on Nations vs. <sfat+Nation> and Nations vs. <lshon+Nations>
without the other three attributes. Out of 1,000,000 permutations, the correct matching in
the sfat test ranked 536 which is very good but for the lshon
test the rank is 765,353 - that is totally insignificant.
So what they did is present a scheme that said they were literally following the Vilna
Gaon thereby eliminating any degrees of freedom. But, in reality, it appears they allowed
a replacement word different from the one that the Gaon used and that isnt even an
exact synonym for the word he used (lshon is closer to dialect or manner of speaking
and sfat to language). While the Gaons choice leads to ELSs with no
significant correlations in the Torah, their replacement does. This substitution shows the
extent to which wiggle can make something work. Failing to call this change of wording
from the Gaons presentation to the attention of the reader is a very serious flaw in
the presentation of their research.
Is there a Mesora for Minimal ELSs?
In his reply, Mr. Witztum claims that there is a mesora for the minimal ELS
method that he uses. That is questionable. We, of course, have a mesora that there are
many hidden things in the Torah, but to claim that this is support for the particular
method that Mr. Witztum uses is a considerable stretch.
In all the vast rabbinic literature, the codes proponents present only a single example
of an explicit ELS prior to 1900. This is in the writing of Rabbeinu Bachya who used it
exactly one time. The sequence bet-hey-reish-daled had a special significance to him and
he found it as an ELS with a skip of 42 starting with the first letter in the Torah. This
sequence occurs as an ELS 207,416 times in the Torah .
The minimal ELS skip is not 42 but rather 2 (occurring 4 times). We cannot be sure
why Rabbeinu Bachya picked the non-minimal ELS he did.
The Ramak (Rabbi Moshe Cordovero) in describing various methods of getting information
from the Torah, mentions the word dilug, usually translated jumps or
skips. In the next paragraph, the Ramak says that we do not understand how to apply
the methods he mentions. This is hardly support for the method of minimal ELSs.
Because they have been mentioned at Discovery Seminars and in Satinovers book,
many seem to think that two anecdotes told about the Vilna Gaon and the Ramban involve
ELSs. But this is false. They involve the initial letters and every third letter of words
they do not have equal letter spacing.
How Significant was the Refereeing Process?
Mr. Witztum concedes my point that because referees dont always give papers
extremely careful consideration, the acceptance in a scientific journal is only a weak
indication of the papers correctness. But he says that his paper was different.
First he claims that it passed scrutiny by Persi Diaconis, who all agree is one of the
worlds leading statisticians. In fact ,
while Diaconis did think the paper worthy of publication as a discussion piece
accompanied by a rebuttal, he was doubtful enough about the result that he offered to
write that rebuttal himself. Moreover, at the time he was under the incorrect impression
that the experimenters had used a statistical test he had proposed, when in fact they had
used a completely different test which improved their result (see footnote
39). Recently, Diaconis has become convinced that the paper is totally invalid .
As for the significance of acceptance of the paper, here is what Prof. Robert Kass, the
editor of Statistical Science at the time has to say :
"Although the referees thought carefully about possible sources of error in the work,
no one tried to reanalyze the data carefully and independently to try to uncover the
presumed flaw in the logic" and "the authors work did not go far enough to
make me seriously think, even for a moment, that their results were anything other than
coincidental, and likely due to a subtle flaw in their methodology."
One person Ive discussed my findings with asked: "Are you claiming that the
referees were dorks?" Of course not! But they didnt have all the relevant
information. There is no reason to think they had the necessary training in the Hebrew
language and Jewish history to understand that Rabbis names had wiggle room. Most
importantly, they took at face value the statement that the list of appellations was
prepared based on the search of a standard database. Im sure that if theyd
realized that for 12 of the Rabbis, the appellations didnt even come from that
database and that the list involved lots of arbitrary choices, then they would not have
recommended the paper for publication .
The View of Scientists
The codes proponents claim that they have a scientifically correct proof of the
statistical validity of codes in the Torah. Thus the opinion of scientists and those whose
science is closest to the issues at hand namely statisticians and mathematicians
should be critical. Rabbi Mechanic is not a scientist. Although he has had a few
years of beginning graduate study in physics, Mr. Witztum is not a scientist. Dr.
Satinover is a medical doctor, not a scientist. Mr. Drosnin is not a scientist. Ive
had thirty years and written hundreds of papers in science and I am able to evaluate the
scientific validity of these arguments. I can tell you they are not valid. But you
shouldnt trust my single opinion alone. Science is a communal enterprise, so it is
important to understand that many scientists who have studied the evidence have reached
the same conclusion that I have while the number of scientists vouching for the
correctness of the codes is very limited.
Each year the Annals of Improbable Research awards the IgNoble prize which it describes  as "A good-natured spoof of science and the Nobel Prizes, the
ceremony honors people whose achievements cannot or should not be reproduced." The
awards in 1997 were handed out by four Nobel Laureates at a ceremony at Harvard
University. According to their website "The 1997 IgNoble prize for literature went to
Doron Witztum, Eliyahu Rips and Yoav Rosenberg of Israel, and Michael Drosnin of the
United States, for their hairsplitting statistical discovery that the Bible contains a
secret, hidden code". Of course, we know that we are supposed to ignore the
opinion of the scoffers of Torah, but Torah codes are not Torah . They are claimed to be science, so the fact that the highest
level of the scientific community regards them as silly is important.
But you may say, do we know if the IgNoble Prize Committee studied the work in detail?
Wouldnt it be better to hear from scientists who can vouch that they have personally
studied the evidence? In fact, there is a petition on the Caltech website  that has two strong requirements for
signatories: they must be professional mathematicians (defined as holding a PhD. in
Mathematics or holding faculty position in Mathematics or Statistics department at a
college or university) and they must "have themselves examined  the evidence and found it entirely unconvincing". The
petition itself summarizes the problems that I called the basic points above.
At the time Im writing, forty-five mathematicians have signed this petition. More
than 10 are frum. Five are members of some countrys National Academy of Science. At
least ten of them are professional statisticians. One (John Allen Paulos) is the author of
a book (Innumeracy) devoted to misuses of numerical arguments.
What about the other side? How many professional mathematicians would be willing to
sign a petition that took the opposite position that "they have themselves examined
the evidence and found it entirely convincing"? 
The Aish website  claims about the Statistical Science paper
"Since its publication over two and a half years ago, world-class statisticians and
Bible scholars have reproduced and verified these results". To a trained scientist,
there are two main issues in evaluating the validity of the WRR paper validating
the procedure used to pick the data and validating the correctness of the method used to
analyze the data. There is, of course, a third purely mechanical issue namely given
the data and given the method, was the data plugged into the method correctly. While this
certainly needs to be checked, I certainly wouldnt have thought "reproducing
and verifying these results" meant only checking that the arithmetic was done
correctly. Nor, Id bet, would you. But in his article, Rabbi Mechanic says
thats all he meant by verified the results. Indeed, the only names of professional
mathematicians or statisticians that he provides as reproducing and verifying these
results are Dr. Brendan McKay and Dr. Alexander Pruss ,
both of whom examined the WRR paper in detail. They concluded that the method and data
were flawed and that, indeed, the arithmetic was done properly when the flawed data was
plugged into the flawed method.
So these "world class statisticians" arent going to sign a petition
that they find the evidence convincing indeed, both have signed the petition that
they find the evidence entirely unconvincing.
In discussing individuals who have "gone on record attesting to the seriousness
and quality of the research", Rabbi Mechanic names three professional mathematicians:
Prof. David Kazhdan of Harvard, Prof. Israel Aumann of Hebrew University and Prof. Daniel
Michelson of the Weizmann Institute. Professor Rips is a fourth professional mathematician
who might be a candidate to state he is convinced by the evidence.
Professor Kazhdan asked me to pass the following on to Rabbi Mechanic: "I am sorry
to say but the quote from the Modesto Bee newspaper of November 4, 1995 is taken out of
the context. I have never checked the results of the paper in Statistical Science and have
never claimed the validity of the theory of codes." So I dont think hed
sign a statement that the evidence convinces him .
Prof. Aumann in an email written on September 21, 1997 wrote about the codes "I
tend to think that theyre nonsense" despite being officially undecided.
So we are left with two professional mathematicians, Profs. Rips and Michelson, both of
them authors of research claiming the validity of codes, who might be willing to say
theyve found the evidence convincing and forty-five who have stated: The
signatories to this letter have themselves examined the evidence and found it entirely
I believe when they began using it, Aishs claim to the public that the codes have
been scientifically proven was well meant. I think they honestly believed this was the
position of those scientists who had looked at the evidence. Rabbi Mechanic, it should be
clear to you that this is not now the position of the scientific world. You cannot
continue to use this claim unless, of course, you believe it is permitted to compromise on
truth to get a Jew to keep Shabbos.
In closing Id like to note the following teshuva of the Rashba : "Yisrael the inheritors of truth, descendants of
Yaakov the Man of Truth, zera emes, would prefer to suffer continued exile and its
horrors rather than accept something without critically and thoroughly analyzing it, step
after step, to separate out anything of doubtful validity...even when it appears to be
miraculous and absolute!"
In the preparation of this article, I benefited from discussions with Mr. Alec Gindis,
Dr. Brendan McKay and Dr. Martha Simon. As always, my Rebbi, Rabbi Yitzchak Adlerstein was
a tremendous source of chizuk, sound advice and necessary piskei halacha.
Please note that this article is copyright, 1998 by Barry Simon, © all rights
Rabbi Mechanic (in his article in Jewish Action;
claims that "Cryptologic mathematics is without question the domain of expertise most
pertinent to assessing the Codes". But, the only thing that the codes that
cryptologists study have in common with the codes used by Witztum et al is the use of the
word "codes". It is Statistics that is most relevant to the Torah codes debate.
 The original article was written in draft
form in mid-August 1997 but delayed in publication to allow the replies of Rabbi Mechanic
and Mr. Witztum to be written. The first draft of the present piece was written in
 I have even done some experiments of my
 I am so disturbed by the acceptance of
these ideas in some parts of our community (based on misunderstandings and on
misstatements about their acceptance by scientists) that I am prepared to give public
lectures on the subject.
 The replies of Rabbi Mechanic (see http://www.aish.edu/issues/biblecodes/s-mechanic.htm)
and Mr. Witztum (see http://www.aish.edu/issues/biblecodes/s-witztum.htm)
rather than focusing solely on the intellectual issues contain numerous personal attacks
on me. There is a tremendous temptation to reply to them here point by point but Ill
instead discuss the issues of true importance. Those who wish to see my reply to the more
personal aspects of their articles can consult http://wopr.com/biblecodes/codes_and_me.htm.
(Note: the complete version of this part of the site is only expected to be ready in late
May; a short version is there now).
 Some of the time, the code searchers look
for ELS that are minimal not over the entire text but a subset of it without ever
enunciating a clear rule when one is allowed to do this.
 In my earlier article, I called
these "word pairs" but since Ill discuss clusters with more than two
members, Ill call them "word clusters" here.
 In my original article, and here a little
later, I discussed the Nations experiment which uses a similar methodology to the Famous
 D. Witztum, E. Rips and Y. Rosenberg, Equidistant
Letter Sequences in the Book of Genesis, Stat. Science, 9, (1994) 429-438; this
article is available on the web at http://www.fortunecity.com/tattooine/delany/11/genesis.html
 This is not to say there arent
others, for example, the fact that the text of the Torah today is not identical letter by
letter to what was given at Mt. Sinai. For space reasons, Ill focus here on these
three but see other articles on my web site for discussion of additional issues.
 The leading nun is the only
circled letter on the last line and the reish is the only circled letter on the fifth line
from the bottom. Now follow the diagonal upwards. See http://cs.anu.edu.au/~bdm/dilugim/candles/
where a more detailed analysis can be found.
 The section of text shown in the
picture is about 1.3% of the standard test text making this an extremely compact example.
 This translation is popular as a text
in which to look for ELSs because it was first used by Witztum, Rips and Rosenberg in
their famous Rabbis paper as a test document. They used the first 78,064 letters of this
Hebrew translation -- 78,064 is the number of letters in Bereishit.
 The example is described in Daniel
Michelson, Codes in the Torah: Reading with Equal Intervals, BOr HaTorah,
6, (1987), 7-39. It is discussed for about 4 pages in Satinovers book. Michelson
makes it clear that he is describing an experiment which was done by Rips.
 Bereishit 2:7-3:3.
 Dr. McKay, a Member of the Australian Academy
of Science and researcher at Australian National University is an expert in combinatorics
and computer science.
 Random permutations destroy the relationship
between letters that is behind any ELS. To be sure that no one would make the nonsensical
claim that this was a residual of the source of the letters, I did the test I describe in War
 That is, I used letters 1975-3061 in War
 These estimates make the assumption that
permutations of the basic text produce equally likely examples of "a random
text". Since there is no real model of random text and the Torah is anything but
random, there is no clear model one can use to justify this assumption nor the similar
assumption on equal probabilities after permutation of lists in the paper of Witztum et al
(see footnote 10). Since Michelson estimated a probability, Ive quoted one based on
the best model one has but from one point of view, all probability estimates
including this one, are bogus.
 The author of the best seller The Bible Codes.
I note that Aish, Mr. Witztum and Prof. Rips all claim that Drosnins work is an
incorrect use of their ideas but Im hard pressed to find much difference between the
examples in Satinovers book Cracking the Bible
Code, which they quote approvingly, and those in Drosnins. And the errors in
Drosnin and Satinover are only somewhat worse than those in Mr. Witztums own word
 Unlike all the other ELSs mentioned
here, those in Moby Dick are in English.
 I sent Mr. Witztum a FAX asking how he
arrived at his probability figure but he did not reply.
 There are many more examples although
space prevents me from giving more.
 This abbreviation is so common, that
many readers would automatically look for it rather than the written out expression.
Witztum, himself, has used abbreviations for long expressions.
 A clear discussion (for mathematically
trained readers) of these and other problems with the probability calculations in word
clusters is presented by Prof. Robert Haralick at the web site http://members.xoom.com/bcodes/haralick.htm.
While Prof. Haralick is presented by Rabbi Mechanic as a codes proponent, it is clear from
his various writings that he is far from convinced of their validity. He has criticized
the probability calculations and the method of statistical analysis used in the famous
Rabbis experiment. He accepts the criticism of the choice of appellations enough to be
trying to organize a totally fresh test. While he is not yet convinced that there
arent codes in the Torah neither is he convinced that the claimed proofs are valid.
 To understand this issue, take a US $5 bill
out of your pocket. It has an eight digit serial number on it. Assuming the digits are
random, the probability of the particular sequence of numbers on your bill is 1 out
of 100 million. So youd need about $500 million in your wallet to have a reasonable
chance of coming up with the particular sequence on the bill in your hand. You dont
have that kind of money there Ill bet but still you had that particular
sequence. The point is that computing probabilities after the fact is problematic.
 The Famous Rabbis experiment is
complicated and there are many problems with it. Here Ill briefly summarize the
experiment and its most serious problems. On this website youll find a much more
complete analysis (in preparation).
 Because of the need for ELSs, WRR only
consider short appellations with a maximum of 8 letters. While everyone would understand
that Rav Moshe ben Maimon meant the Rambam, I dare say many if asked who was Rav Moshe
would think of Rav Moshe Feinstein, not the Rambam. This issue of ambiguity effects other
appellations. Moreover, you might ask yourself why it is reasonable to restrict to short
appellations. If the phenomenon is due to chance, it is understandable that a long phrase
such as Rav Moshe ben Maimon wont occur but if G-d were encoding names, why would He
be restricted to shortened versions?
 I am not saying that this is because of
a deliberate intention to deceive but the results are usually presented without many
mathematical details so the fact remains that many do have this impression.
 In order to follow the approach of WRR,
Dr. McKay restricted the search to date forms that were 5-8 letters.
 That is, one can certainly construct
test texts where the precise phenomena that I describe occurs. Im unsure if such
extreme cases occur in Bereishit itself but pairs that you and I would think were quite
close can be regarded according to the c-value measure as further apart than pairs we
would think of as quite distant.
 That is one close to the start of
Bereishit and one close to the end.
 WRR choose certain ELS skip sizes to
assure that on average, 10 ELSs arise in their process. Ive assumed in my
calculation that each time this is done, precisely 10 arise. For those who want to
understand where the 6 million figure comes from, the quantity they call delta(e,e)
requires you to measure 27 distances (5x5 to get a their quantity l and two more for f and
f). Their sigma requires you to do this 20 times. Their quantity omega requires you
to compute 10x10=100 different sigmas. The c-value requires you to compute 125 omega
values. You then need to multiply 27x20x100x125=6,750,000 to figure out the number of
distances to compute for a single c-value.
 Mr. Witztum claims that they used
a method proposed by Persi Diaconis to compute the statistics. This is false. Diaconis
requested two changes in their approach and they only followed one of them. The other
change would have decreased their statistic by a factor of hundreds.
 According to an email that Prof.
Haralick sent me.
 According to Prof. Havlins
statement referenced in the next footnote.
 The response can be found at http://www.torahcodes.co.il/havlin.htm.
This document was prepared in 1996 fully 10 years after the list was prepared.
 BNMK do not claim that they arrived at
their list by a priori means; their claim is only that a list that is as reasonable as the
one in WRR can flip the texts in which the correlations do and do not occur. Its a
demonstration that the wiggle room in the appellations can explain everything.
 There is an issue mentioned in Rabbi Mechanics reply
that needs to be addressed in the context of this discussion. He reports that Mr. Gans had
a conversation with me in which he told me that he had "successfully completed"
an experiment on correlations between Rabbi appellations and cities (In fact, what Mr.
Gans told me is that he had some intriguing preliminary results that definitely required
further checking. Indeed, he invited me by email shortly afterwards to help with this
process. I note that now, nine months later, the results of this experiment which was
supposed to have been completed in June have not been made available to me or to the
public. On March 24, 1998, Mr. Gans released a public statement that says: "That
investigation is extremely detailed and is not yet complete". It is certainly not
reasonable to claim the result as "successfully completed" in these
circumstances.). Furthermore, Rabbi Mechanic states that Mr. Gans wrote up a report which
stated that "Dr. Simon understood that were it indeed found to be without flaw, it
would unequivocally confirm that there could not have been any data manipulation in the
Famous Rabbis experiment." Obviously I cant comment on what Mr. Gans wrote to
Rabbi Mechanic nor what he thought Id understood but I can state that the
implication that I agreed to this logic is totally false. Given that I didnt have
any of Mr. Gans data to study, I was totally non-committal in my responses. Moreover, if
Mr. Gans had stated anything as explicit as Rabbi Mechanics statement, I would have
objected. Indeed, an experiment of the kind Rabbi Mechanic describes doesnt change
the subjective nature of the appellation list in the original experiment and doesnt
change the resulting invalidity of that experiment. For a new experiment, the list of
Rabbis appellations is a priori although still subjective so at best the experiment
says as much about the list as Bereishit. Of course, the real point is that once such an
experiment is made available, one will need to look carefully to see if all the
Rabbis appellations were used (or just a convenient subset) and, most importantly,
one would need to examine how much wiggle room there is in the choice of cities, their
spelling and the variants used.
 There are some codes critics that have
made accusations of dishonesty just as there are codes proponents who have questioned the
integrity and motives of the codes critics. I will have no part of either kind of public
attack. As noted by Rabbi
Mechanic, I have even gone on public record decrying one such attack on Rips and
Witztum in the Notices of the American Mathematical Society; see http://www.ams.org/notices/199711/letter-simon.html
 For a detailed analysis of the major
flaws in this experiment see the article by three mathematicians (Dror Bar- Natan, Brendan
McKay and Shlomo Sternberg) posted on the web at http://cs.anu.edu.au/~bdm/dilugim/Nations/
 That is where the famous Rabbis
experiment had two columns, one with Rabbis appellations and one with their dates,
this experiment had two columns also. One had names of nations like Magog and Canaan. The
other had attributes like "the language of Magog". For the true text they lined
up the nations next to their attributes whereas the permuted test might for example line
up Magog against the language of Canaan. There is a small technical difference in that
they look for nations as ELS with skip 1 (plain text) or 1 and the attribute+nation
as ELSs and this requires a change in the way they define c-values.
 The full quote from the Vilna Gaon is
included in the article of Bar-Natan, McKay and Sternberg posted at http://cs.anu.edu.au/~bdm/dilugim/Nations/
 The effect is not explained totally by
this single wiggle; see the fuller discussion of Bar-Natal et. al for other problems. I
focus on this because it is such a clear misuse of wiggle.
 This may seem like such a large number
that it indicates an anomalously large number of ELSs in the Torah. In fact it is about 1%
less then would be expected on the basis of word frequencies alone. This just shows how
often short words occur as ELSs.
 This sentence is based on a letter from
Prof. Diaconis which, because it is such an important point, I have confirmed in email
with Prof. Kass. I also have a letter from Prof. Aumann to Prof. Diaconis dated August 28,
1992 that says: "You told me that you had spoken to the editor of Statistical Science
and had recommended to him that the paper submitted by Rips et al to that journal be
published, with the proviso that a discussion by an independent discussant also be
 As can be seen from his signing the
petition Ill discuss shortly.
 While I am not claiming there was any
intention to deceive, the fact remains that the abbreviated description in the paper of
how the list of appellations were arrived at gave a false picture of the objectivity of
the process. That this is a problem is acknowledged by Rips and Witztum who have stated
(see Witztums website):
"Because English is not our native language, this version of the paper was rewritten
by an English-speaking scientist. When we reviewed the manuscript, we overlooked the fact
that the description of Professor Havlin's method of compiling the list may be
 A student of Rav Simcha Wasserman, told
me of asking Rav Simcha his opinion of the codes several years ago. Rav Simcha replied
"I don't know but certainly one would not say Birchos HaTorah over them".
 Examining the evidence is indeed
the way scientists confirm results of others. Ive heard that one codes proponent
dismisses some of the petition signers because they havent done any experiments
themselves. This is akin to saying you cant claim the proof of a theorem is
incorrect until youve presented your own incorrect proof. About a fifth of the
petition signers have done their own experiments on codes.
 Note the change from unconvincing to
 Dr. Pruss, who Rabbi Mechainic calls a
"world-class statistician" is a promising young mathematician who got his degree
in 1996. Id certainly not use the term "world-class" for someone just at
the start of their career. This is alas a typical case of the codes proponents overstating
the qualifications of anyone they feel supports any aspect of their position. Dr. Pruss
asked me to include the following statement in his name: "I am quite appalled by the
overblown characterization of my qualifications. In fact, not only am I not a world-class
statistician, but I am not even a statistician: I am a probability theorist." So
despite limiting "verifying the results" to checking arithmetic and despite
having claims on his website about "world-class statisticians" (plural), Rabbi
Mechanic hasnt been able to name a single statistican who verified the results.
 I havent explicitly questioned
the other three signers of the introduction of Witztums book but Rips himself told
me last summer that he didnt think any of them or any other mathematician besides
Michelson was convinced by the evidence. One of the signers of the introduction (Prof.
Hillel Furstenberg) has been quoted in the Jerusalem Report (Sept. 4 1997, pg.18)
as saying that he might not have signed it if hed realized how much freedom there
was in the choice of appellations.
 Teshuvos Harashba, Section 1, 548. I am
grateful to Rabbis Dovid Gottlieb and Matis Weinberg for bringing this to my attention.